Automatic equal phase shift principle for space charge measurement under periodic stress of arbitrary waveform

An automatic equal phase shift principle (AEPS) is proposed to simplify space charge detection under periodic stress with the pulsed electroacoustic method. For pulse frequency, f
_p
is a non-integral multiple with periodic stress frequency f
_a
; the detecting phase can be automatically shifted with a certain value after each cycle of periodic stress. The pulse position will be at the same phase of periodic stress after several cycles. The minimum amounts of periodic stress cycles and pulse generated during this process are defined as N
_a
(>1) and N
_p
, respectively. They can be uniquely confirmed by the characteristic equation N
_a
/f
_a
= N
_p
/f
_p
. Moreover, the positions of pulse generated during this process are equally distributed in the periodic stress from 0
^o
to 360° with a characteristic sequence of pulse. The phase interval, i.e. phase resolution Δ', is 2π divided by N
_p
. Consequently, the phase resolution can be easily enhanced through an increase in the pulse amount N
_p
by selection of f
_p
, according to the characteristic equation. Finally, space charge behaviours in low-density polyethylene under 50 Hz AC stress were measured with three different pulse frequencies f
_p
, i.e. 25.5, 1010 and 1001 Hz, to validate the proposed AEPS principle. Results show that the space charge distribution can be successfully acquired with a phase resolution from 7.07
^o
to 0.36
^o
, even if the pulse frequency is lower than the AC frequency at 25.5 Hz. This result indicates that AEPS can overcome the frequency limitation of the pulse generator, and a high phase resolution can be realised.